High-Dimensional Vector Autoregressive Processes with Local Dependence

• Activity Number: 687
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Michael Schweinberger and Sergii Babkin* and Katherine Bennett Ensor
• Companies: Rice University and Rice University and Rice University
• Keywords: high-dimensional graphical models ; multivariate time series ; vector-autoregressive processes ; local dependence ; local computing ; LASSO

Abstract

We consider high-dimensional multivariate time series with additional structure in the form of spatial structure where dependence is local in the sense that time series which are close in space may be dependent whereas distant time series are independent. Examples are observations of air pollution and temperature recorded by weather stations. We take advantage of the additional structure by introducing a novel two-step estimation approach which exploits local dependence for the purpose of local computing and has both computational and statistical advantages. The two-step estimation approach first estimates the range of dependence and then exploits the estimated range of dependence to estimate local dependencies among time series. If the range of dependence is short and the number of time series is large, the two-step estimation approach results in a massive reduction in computing time and can reduce statistical and prediction error. We discuss finite-sample properties of estimators and present simulation results along with an application to a large multivariate time series.